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Modulus of Rupture.

W\

3 \

It

Moment of diminished section = moment of i rivet + moment of 2 rivets
(a - (4- )}# = *5x arrrn-^xarm

_ (1-394* 8-5)-h(49'i6x 11-25)        

_

-      68-28 -(13-94 -4- 49-1 6)      **

yc being limiting stress (see below), B c and D E are reference
lines, and the areas are found as before.

Each stress area = 26*35    an<^ arm = 2 x"12

For W. I. plate girders t/t= 5 and/c =4.

For Steel plate girders /t= 6 and/c = 5

The reduced jfc being an allowance for buckling.

..    Moment of resistance =/c x area x arm

= 4 x 26*35 x 3i '12 = 2226 ton, ins, for W. I.
= 5 x 26*35 x 21 i2 = 2782 ton, ins, for Steel

Value of f in Beams. If a < solid' beam be broken
.across, the ultimate stress, -deduced by applying the momenta!
formula, will be usualty- found much greater than ft breaking.
If then, the bending theory be pushed as far as the breaking
load, we must meet the case by the value

/o-0/t                        .

where /0 is the stress found by transverse experiment and called
the moduhis of rupture, while O we shall call the bending coefficient.
It varies with the beam section. Thus :

In sections ^ or  ^       O- is greatest, being about 2
In sections   |  or   H       O is less,       being about ij-
In sections *TT                  O = r

but depends also on the material, as seen in the following table
^compiled from experiment), and is often less than unit/ for woods.

TABLE OF BENDING COEFFICIENTS (0) FOR SOLID SECTIONS.

Fir           |    -52 to -94

Oak         |      7 to i *o

Pitch Pine 1    '8 to 2-2

Cast Iron | 2;  2-35;

Wrought Iroa | 1*6;  175
Forged Steel | 1-47;  i'6

Gun Metal     |    i -o;  i '9
         ^ ) where ^=flange width

and &=wtb tkickness

And our beam formula becomes Bm = OfZ*